Turn key, starter doesn't turn

[DrPepper]

I have a 2007 GMC 4.8L 1500 NBS. When the truck is cold, when I turn the key, the starter doesn't turn and I don't hear the solenoid. Sometimes this happens 2 or 3 times before the starter turns. The battery is original, 3 years old. When the starter does turn, it's strong and there is no problem starting.
Usually when the truck is warm, there is no problem. It starts w/ the first turn of the key.
Does anyone have any ideas why this is happening?